Asymptotic and scattering behaviour for degenerate multi-solitons in the Hirota equation

Cen, J. & Fring, A. ORCID: 0000-0002-7896-7161 (2019). Asymptotic and scattering behaviour for degenerate multi-solitons in the Hirota equation. Physica D: Nonlinear Phenomena, 397, pp. 17-24. doi: 10.1016/j.physd.2019.05.005

Abstract

We construct all higher order conserved charges from a general two-dimensional zero curvature condition using a Gardner transformation. Employing twoof those charges in the definition of a Hamiltonian allows to view theHirota equationsas an integrablePT-symmetric extension of the nonlinear Schrödinger equation. Weconstruct new degenerate multi-soliton solutions from Hirota’sdirect method as well asDarboux-Crum transformations based on Jordan states. We study the properties of thesesolutions, computing their asymptotic time-dependent displacements and also show thattheir scattering process has a distinct characteristic behaviour different from the nonde-generate counterparts allowing only for interactions of absorb-emit type.

Publication Type:	Article
Additional Information:	© 2019 Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords:	Hirota equation, PT-symmetry, Darboux-Crum-Crum transformation, Multi-soliton solutions
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Departments:	School of Science & Technology